Note: Intro -- Preface -- General References -- Acknowledgements -- Contents -- Contributors -- Acronyms -- Symbols -- 1 Introductory Notes on the Josephson Effect: Main Concepts and Phenomenology -- 1.1 A Brief Historical Survey on the Materials Used for the Realization of Superconducting Junctions -- 1.2 The Coupling Between Macroscopic Quantum Systems and the Equations of the Josephson Effect -- 1.2.1 Josephson Equations in the Tunnel Limit -- 1.2.2 Different Types of Josephson Junctions Other than Tunnel -- 1.3 The Tunneling Hamiltonian and the Scattering Formalism -- 1.3.1 Expression for the Total Current in the Tunneling Hamiltonian Formalism -- 1.3.2 Conductance in a Tunnel Junction -- 1.3.3 From the Tunneling Transfer Hamiltonian to the Scattering Formalism -- 1.3.4 Andreev Reflection -- 1.3.5 Josephson Effect Derived from Quasi-particle Andreev Bound States -- 1.4 Current-Voltage (I-V) Characteristics: From Microscopic Theory to the Resistively Shunted Junction Model -- 1.4.1 I-V: Notes on the Resistively Shunted Junction Model -- 1.5 Temperature Dependence of Ic Rn and of the I-V characteristics -- 1.5.1 Temperature Dependence of Ic in the Tunnel Limit -- 1.5.2 Temperature Dependence of Ic Other than the Tunnel Limit -- 1.6 Magnetic Field Effects -- 1.7 Electrodynamics of the Josephson Junction -- 1.8 Material and Nano Science Open Novel Routes for the Fabrication of Josephson Junctions -- 1.8.1 Low Temperature Josephson Junctions -- 1.8.2 High Temperature Josephson Junctions -- 1.8.3 Hybrid Junctions -- References -- 2 Josephson Devices as Tests of Quantum Mechanics Towards the Everyday Level -- 2.1 Background -- 2.2 Early History -- 2.3 Consolidation: Work on MQT in the Early 80s -- 2.4 Progress Towards MQC: 1981-1999 -- 2.5 The Modern Era: Josephson Qubits -- 2.6 Where Do We Stand? -- References. , 3 Basic Properties of the Josephson Effect -- 3.1 Introduction -- 3.2 Basic Features and Fundamental Relations -- 3.3 Josephson Effect in Basic Types of Junctions -- 3.4 SNS Junctions -- 3.4.1 Dirty Limit -- 3.4.2 Clean SNS Junctions -- 3.5 Double Barrier SINIS Junctions -- 3.5.1 SINIS Junctions, Clean Limit -- 3.5.2 SINIS Junctions, Dirty Limit -- 3.6 SFS Josephson Junctions -- 3.6.1 Proximity Effect in SF Bilayer -- 3.7 CPR in SFS Junctions -- 3.7.1 -Junctions -- 3.7.2 0-Junctions -- 3.7.3 CPR in Serial SIsFS and SFsFS Junctions -- References -- 4 Charge Transport in Unconventional Superconductor Junctions -- 4.1 Topological Superconductivity -- 4.1.1 Pair Potential -- 4.1.2 Topological Number and Surface Bound States -- 4.1.3 Tunnel Conductance -- 4.1.4 Josephson Current -- 4.2 Proximity Effect in a Dirty Normal Metal -- 4.2.1 Conductance of a Dirty NS Junction -- 4.2.2 Josephson Effect in a Dirty SNS Junction -- 4.3 Remark: Odd-Frequency Cooper Pair and Majorana Fermion -- References -- 5 Mesoscopic Features in Nanoscale Superconducting Devices -- 5.1 Introduction -- 5.2 Proximity in Macroscopic Systems -- 5.2.1 Free Energy of the Isolated Superconductor -- 5.2.2 Superconducting Correlations Induced in a Normal Metal by Proximity -- 5.3 Andreev Resonances at Superconductor-Normal Metal Interfaces -- 5.3.1 Andreev Resonances in a Clean N Slab in Proximity with a Superconductor -- 5.3.2 Diffusive N/S Boundary -- 5.3.3 Andreev Reflection Under the Magnetic Field: Magnetoconductance Oscillations in N/S Junctions -- 5.4 Scattering Approach to Ballistic Transport in SNS Josephson Junctions -- 5.4.1 Andreev Bound States with Fully Transmitting NS Interfaces -- 5.4.2 Density of Energy States at a Generic SNS Junction -- 5.5 Ballistic and Diffusive SNS Junction Systems -- 5.5.1 Ballistic Short and Long SNS Junctions. , 5.5.2 Diffusive Short and Long SNS Junctions -- 5.6 Semiclassical Approach to Diffusive Systems and Other Signatures of the Mesoscopic Regime -- 5.6.1 Minigap in SNS Diffusive Junctions -- 5.6.2 Low-Temperature Reentrant Behavior of the Resistance in a Diffusive N Wire in Proximity with a Superconductor -- 5.6.3 Resistance Change in a Wire in Contact with a Superconducting Electrode -- 5.7 Mesoscopic Conductance Fluctuations -- 5.7.1 Self Correlations of the Conductance in Magnetic Field -- 5.7.2 Self Correlations of the Conductance in Non Equilibrium -- 5.8 From Few to Single Channel Junctions -- 5.8.1 Shot Noise in Few Channel NS Junctions -- 5.8.2 Single Channel SS Junctions -- 5.8.3 Andreev Qubits and Parity Jumps -- 5.8.4 Transient Dynamics -- References -- 6 Magnetic Field Effects in Josephson Junctions -- 6.1 Introduction -- 6.2 Static Magnetic Fields -- 6.2.1 Flux Focussing -- 6.2.2 Time-Independent Sine-Gordon Equation -- 6.2.3 Magnetic Interference Patterns -- 6.2.4 Josephson Vortices -- 6.3 Time-Dependent Magnetic Fields -- 6.3.1 Time-Dependent Sine-Gordon Equation -- 6.3.2 Fiske Steps -- 6.3.3 Zero-Field Steps -- References -- 7 Current-Voltage Characteristics -- 7.1 The Resistively Shunted Junction Model -- 7.1.1 The Noise Term in the RSJ Model, a First Watch at Fluctuations -- 7.2 I-V Curves in the RSJ Model in the Small Capacitance Limit -- 7.3 I-V Curves in the RSJ Model for Finite Capacitance -- 7.3.1 Details of the I-V Curves in the Subgap Region for Finite Capacitance and Nonlinear RSJ Models -- 7.4 Current Biased Tunneling Junction, a More Accurate Description of the Subgap Region for Finite Capacitance -- 7.5 Effects of Thermal Fluctuations -- 7.5.1 Negligible Capacitance -- 7.5.2 Finite Capacitance -- 7.5.3 Large Capacitance -- 7.6 I-V Curves: When They Do Not Match RSJ-Like Predictions. , 7.6.1 Deviations from RSJ, RSJN and TJM Models -- 7.6.2 I-V Curves in Small or Nanoscale Junctions: From the RSJ Model to Phase Diffusion -- 7.6.3 Beyond Classical Smoluchowski Dynamics, from Coulomb Blockade to Quantum Diffusion -- 7.6.4 More on the Amplitude of the Hysteresis -- 7.6.5 Concluding Remarks and a Further Look at Experimental I-V Curves -- References -- 8 High Critical Temperature Superconductor Josephson Junctions and Other Exotic Structures -- 8.1 Introduction -- 8.2 Complementary Investigations and the Importance of a Structural Feedback -- 8.3 Grain Boundary Junctions -- 8.3.1 Bicrystal Junctions -- 8.3.2 Biepitaxial Junctions -- 8.3.3 Step-Edge Junctions -- 8.4 Locally Affecting Superconductivity, Moving Oxygen in Thin Films and Damaged Junctions -- 8.4.1 Modifying Junctions by Irradiation -- 8.4.2 Electro-Migration Studies -- 8.5 Junctions with an Artificial Barrier -- 8.5.1 Ramp Edge Junctions Realized with Au and Ag Inert Barriers -- 8.5.2 Ramp Edge Junctions Realized with Perosvkite and Layered Materials -- 8.5.3 Trilayer Structures -- 8.6 Interface-Engineered Junctions, a different way of Creating a Barrier -- 8.6.1 Ramp-Edge Junctions for Superconducting Electronics -- 8.7 Junctions with HTS Other Than YBCO -- 8.7.1 La1.85Sr0.15CuO4-Based Trilayer with One-Unit-Cell-Thick Barrier -- 8.7.2 Electron Doped HTS -- 8.8 Intrinsic Stacked Junctions -- 8.9 HTS Junctions and Wires on the Meso/nano Scale -- 8.9.1 GB Junctions Realized with Ultra-Thin Films and Superlattices -- 8.9.2 HTS Nanostructures and Nanowires -- 8.9.3 Submicron Josephson Junctions, Energy Scales and Mesoscopic Effects -- 8.10 General Criteria on I-V Curves and the Estimation of Junction Parameters -- 8.10.1 The Shape of I-V Curves -- 8.10.2 From I-V Curves and Their Modelling to Junction Parameters. , 8.10.3 Capacitance and Related Electromagnetic Properties of Junction Interfaces -- 8.11 Dependence of the Josephson Current on the Temperature -- 8.12 Notes on the Magnetic Properties of HTS Junctions -- 8.12.1 Dependence of the Critical Current and I-V Characteristics on the Magnetic Field -- 8.12.2 Spontaneous Magnetization with Random Orientation -- 8.13 Fractional Shapiro Steps: Time-Dependent Effects -- 8.14 Other Exotic Structures: Josephson Junctions Based on Interface Superconductors -- References -- 9 Pairing Symmetry Effects -- 9.1 Dependence of Josephson Critical Currents on Junction Geometry -- 9.2 Quantum Interference of Josephson Currents -- 9.3 Spontaneous Josephson Currents -- References -- 10 Intrinsic Josephson Junctions in High Temperature Superconductors -- 10.1 Introduction -- 10.2 Fabrication Methods and Materials -- 10.3 Basic Properties -- 10.3.1 Resistivity and Out-of-Plane Critical Current Density -- 10.3.2 Current Voltage Characteristics -- 10.3.3 Interlayer Tunneling Spectroscopy -- 10.3.4 Modelling of One-Dimensional Stacks: Coupling by Charge Fluctuations -- 10.4 Josephson Plasma Oscillations and Collective Fluxon Dynamics -- 10.4.1 Coupled Sine-Gordon Equations -- 10.4.2 Static Josephson Fluxons Lattices -- 10.4.3 Collective Josephson Plasma Oscillations -- 10.4.4 Fluxon Dynamics -- 10.5 Generation of THz Radiation with Intrinsic Junction Stacks -- References -- 11 Phase Dynamics and Macroscopic Quantum Tunneling -- 11.1 Escape Out of a Metastable State -- 11.1.1 Theoretical Background, Effects of Dissipation and the Underdamped Limit -- 11.1.2 The First Experiments -- 11.1.3 The Effect of the Magnetic Field on SCD -- 11.1.4 Notes on Resonant Activation and Quantized Energy Level -- 11.1.5 The Master Equation for Phase Dynamics -- 11.1.6 The Retrapping Current. , 11.1.7 Thermal Activation and Macroscopic Quantum Tunneling in SQUIDs and Annular Junctions.

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